Chesley

2021-10-24

To calculate:
To simplify the expression $\sqrt[3]{-8{x}^{3}}$.

Usamah Prosser

Calculation:
According to quotient property of square root $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$.
And the product property of square root states $\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}$
This can be written as $\sqrt[3]{-8{x}^{3}}=\sqrt[3]{\left(-2\right)×\left(-2\right)×\left(-2\right)×x×x×x}$
$\sqrt[3]{-8{x}^{3}}=\sqrt[3]{\left(-2{\right)}^{3}×{x}^{3}}$
Applying the product rule,
$\sqrt[3]{-8{x}^{3}}=\sqrt[3]{\left(-2{\right)}^{3}}×\sqrt[3]{{x}^{3}}$
$\sqrt[3]{-8{x}^{3}}=\left(-2\right)×x$
$\sqrt[3]{-8{x}^{3}}=-2x$

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